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| The Change-Base Issue for $\Omega$-Categories |
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Citation： |
Chengling FANG,Dexue ZHANG.The Change-Base Issue for $\Omega$-Categories[J].Chinese Annals of Mathematics B,2008,29(4):341~352 |
| Page view： 1299
Net amount： 751 |
Authors： |
Chengling FANG; Dexue ZHANG |
Foundation： |
the National Natural Science Foundation of China (No. 10771147) and the Program for New Century Excellent Talents in University (No. 05-0779). |
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| Abstract： |
Let $G:\Omega\lra\Omega'$ be a closed unital map between commutative,unital quantales. $G$ induces a functor $\overline{G}$ from thecategory of $\Omega$-categories to that of $\Omega'$-categories. This paper is concerned with some basic properties of $\overline{G}$.The main results are: (1) when $\Omega$, $\Omega'$ are integral,$G:\Omega\lra\Omega'$ and $F:\Omega'\lra\Omega$ are closed unital maps,$\overline{F}$ is a left adjoint of $\overline{G}$ if and only if$F$ is a left adjoint of $G$; (2) $\overline{G}$ is an equivalence of categories if and only if $G$ is an isomorphism in the category of commutative unital quantales and closed unital maps; and (3) a sufficient condition is obtained for $\overline{G}$ to preserve completeness in the sense that $\overline{G}A$ is a complete $\Omega'$-category whenever $A$ is a complete $\Omega$-category. |
Keywords： |
Commutative unital quantale, Closed unital map, Enriched category, Change-base |
Classification： |
18D20, 18A35, 06F07, 18B35 |
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